Study of <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> nuclei in variation-after-projection framework

Variation-after-projection (VAP) calculations in conjunction with the Hartree- Bogoliubov (HB) ansatz have been carried out for A = 68-88, N = Z nuclei. In this framework, the yrast spectra with , B(E2) transition probabilities and deformation parameter ( ) have been obtained. A pairing interaction for like particles as well as protons and neutrons has been included in the model for a two-body interaction.Received: 28 April 2003, Revised: 20 March 2004, Published online: 14 September 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.60.-n Nuclear structure models and methods - 27.50. + e      

The <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis><Emphasis Type="Italic">f</Emphasis><Subscript>7/2</Subscript>-shell nuclei: Experimental highlights

During the last decade, as the experimental and computing means and techniques have rapidly evolved, the experimental investigation of the f_7/2-shell nuclei has gained renewed interest. TheN = Z nuclei studied with the GASP array range from ⁴⁴Ti to ⁵²Fe. The results extended the knowledge of their structure up to high spins and excitation energies, above band terminations, where the competition with the charged-particles emission was initially thought to obscure the possibility of gamma-ray spectroscopy investigation. The paper highlights some of the most outstanding properties of these nuclei such as the nuclear rotation and backbending effects, band termination states, yrast traps, non-natural parity bands, competition between T = 0 and T = 1 pn pairing modes.Received: 30 October 2002, Published online: 16 March 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.60.Cs Shell model - 23.20.Lv transitions and level energies - 27.40. + z C.A. Ur: On leave from NIPNE Bucharest, Romania     

Forward on the <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> line with GASP

The experimental study of the proton-rich nuclei close to the N = Z line is a constant challenge for nuclear spectroscopy, mainly due to the difficulty to produce them with the currently available beam/target combinations. Significant advances on this direction were obtained from experiments performed with the GASP array during the last two years: the yrast line of ⁸⁴Mo was extended up to 10 ⁺ , ⁸⁸Ru observed for the first time, and the N = Z + 1 line was mapped from ⁸¹Zr to ⁹⁵Ag. These new results allow us to have a more complete image of the transition from the well-deformed shell closure at N,Z = 40 to the spherical-shell closure at N,Z = 50, and highlights some particular effects that can be observed only in the vicinity of the N = Z line.Received: 10 January 2003, Published online: 23 March 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Pc Single-particle levels and strength functions - 21.10.Re Collective levels - 23.20.-g Electromagnetic transitions     

Projected shell model study on nuclei near the <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> line

Study of the nuclei in the mass-80 region is not only interesting due to the existence of abundant nuclear-structure phenomena, but also important in understanding the nucleosynthesis in the rp-process. It is difficult to apply a conventional shell model due to the necessary involvement of the g_9/2 sub-shell. In this paper, the projected shell model is introduced to this study. Calculations are systematically performed for the collective levels as well as the quasi-particle excitations. It is demonstrated that calculations with this truncation scheme can achieve a comparable quality as the large-scale shell model diagonalizations for ⁴⁸Cr, but the present method can be applied to much heavier mass regions. While the known experimental data of the yrast bands in the nuclei (from Se to Ru) are reasonably described, the present calculations predict the existence of high-K states, some of which lie low in energy under certain structure conditions.Received: 30 October 2002, Revised: 25 January 2003, Published online: 23 March 2004PACS: 21.60.-n Nuclear structure models and methods     

<Emphasis Type="Italic">Z</Emphasis>-scan study of the thermo-optical effect

In the case of cw Gaussian illumination, the thermo-optical n₂ cannot be characterised by a constant value. It is shown that, if absorption has both linear and nonlinear contributions, the thermo-optical n₂ consists of a position- and power-dependent term. Hence analytical formulae that assume a constant n₂ are no longer valid for the Z-scan fitting. In this paper a new Z-scan theory is introduced, which is applicable to the thermo-optical effect in the presence of both linear and nonlinear absorption and an arbitrary extent of optical nonlinearity. The calculation technique can be used for large sample thickness too, by dividing it into thin slices. It was found that inside one slice, the distribution of the light-induced refraction is similar to that for the case of graded index media. The propagation can be described through the transformation of the q-parameter. It is demonstrated that the Z-scan technique makes the sensitive measurement of the linear absorption coefficient possible. The linear and nonlinear absorption coefficients were experimentally determined for Mg doped LiNbO₃ to be =0.6 m^-1 and =2.9×10^-9 m/W, respectively. PACS 42.79.Ry; 78.20.Nv; 77.84.Dy     

<Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> from the lattice with Wilson quarks

We report our results for the bag parameter B _K obtained from the quenched simulations on the lattice with Wilson fermions for three values of the lattice spacing. We implemented the method by which no subtraction of the mixing with other four-fermion operators is needed. Our final result, in terms of the renormalization group invariant bag parameter, is .Received: 9 July 2004, Revised: 27 July 2004, Published online: 21 September 2004     

<Emphasis Type="Italic">V</Emphasis>-<Emphasis Type="Italic">A</Emphasis> sum rules with <Emphasis Type="Italic">D</Emphasis> = 10 operators

The difference of vector and axial-vector charged current correlators is analyzed by means of QCD sum rules. The contribution of 10-dimensional 4-quark condensates is calculated and its value is estimated within the framework of the factorization hypothesis. It is compared to the result obtained from an operator fit of Borel sum rules in the complex q ²-plane, calculated from experimental data on hadronic -decays. This fit gives accurate values of the light quark condensate and the quark-gluon mixed condensate. The size of the high-order operators and the convergence of the operator series are discussed.Received: 10 May 2004, Revised: 7 September 2004, Published online: 18 November 2004     

<Emphasis Type="Italic">B</Emphasis> and <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript> decay constants from moments of finite energy sum rules in QCD

We use an appropriate combination of moments of finite energy sum rules in QCD in order to compute the B _q -meson decay constants f _B and . We perform the calculation using a two-loop computation of the imaginary part of the pseudoscalar two point function in terms of the running bottom quark mass. The results are stable against the so-called QCD duality threshold, and they are in agreement with the estimates obtained from Borel transform QCD sum rules and lattice computations.Received: 28 July 2004, Revised: 10 September 2004, Published online: 23 November 2004PACS: 12.38.Bx, 12.38.LgSupported by MCYT-FEDER under contract FPA2002-00612.     

Lepton flavor violating <Emphasis Type="Italic">Z</Emphasis>-decays in supersymmetric seesaw model

In the supersymmetric seesaw model, large flavor mixings of sleptons induce the lepton flavor violating (LFV) interactions ( ), which give rise to various LFV processes. In this work we examine the LFV decays . Subject to the constraints from the existing neutrino oscillation data and the experimental bounds on the decays , these LFV Z-decays are found to be sizable, and among them the largest-rate channel can occur with a branching ratio of 10^-8 and may be accessible at the LHC or GigaZ experiment.Received: 1 September 2003, Published online: 20 November 2003     

Jet production in <Emphasis Type="Italic">pA</Emphasis> and <Emphasis Type="Italic">AA</Emphasis> collisions in the perturbative QCD pomeron model

Inclusive cross-sections for gluon jet production are studied numerically in the perturbative QCD pomeron model for pA and central AA collisions at high energies. Two forms for the inclusive cross-sections, with and without emission from the triple pomeron vertex, are compared. The difference was found to reduce to a numerical factor for momenta below the saturation momentum Q _s. Above Q _s no difference was found at all. For pA collisions the gluon spectrum was found to be at momenta k below Q _s and above it. For central AA collisions it was found to be at momenta k below Q _s and above it. At large k the spectrum goes like , flattening with energy. The multiplicities turned out to be proportional to A ^0.7 for pA collisions and A for central AA collisions with a good precision. In the latter case they are becoming more peaked at the center with the growth of energy. Their absolute values are high and grow rapidly with energy in accordance with the high value of the BFKL intercept.Received: 12 October 2004, Revised: 22 November 2004, Published online: 21 January 2005     

<Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">e</Emphasis>3</Subscript> decays and CKM unitarity

We present a detailed numerical study of the K_e3 decays to in chiral perturbation theory with virtual photons and leptons. We describe the extraction of the CKM matrix element |V_us| from the experimental K_e3 decay parameters. We propose a consistency check of the K ⁺ _e3 and K⁰_e3 data that is largely insensitive to the dominating theoretical uncertainties, in particular the contributions of . Our analysis is highly relevant in view of the recent high statistics measurement of the K ⁺ _e3 branching ratio by E865 at Brookhaven which does not indicate any significant deviation from CKM unitarity but rather a discrepancy with the present K⁰_e3 data.Received: 22 January 2004, Published online: 30 April 2004Work supported in part by IHP-RTN, Contract No. HPRN-CT2002-00311 (EURIDICE) and by Acciones Integradas, Project No. 19/2003 (Austria), HU2002-0044 (MCYT, Spain)     

<Emphasis Type="Italic">CP</Emphasis> violation in the 3 jet and 4 jet decays of the <Emphasis Type="Italic">Z</Emphasis> boson at GigaZ

We review CP-violating effects in jet and 4 jet decays, assuming the presence of CP-violating effective and couplings. Longitudinal beam polarization is included in the studies. We propose a direct search for such CP-violating couplings by using various CP-odd observables. The data of a future linear collider running at the Z-resonance in the so-called GigaZ option should give significant information on the couplings. Finally we show that stringent bounds on the mass of excited b quarks can be derived if appropriate couplings are of a size characteristic of a strong interaction.Received: 21 August 2003, Published online: 20 November 2003     

Collective excitations of the element <Emphasis Type="Italic">Z</Emphasis> = 120

The low-lying vibrational excitations of superheavy even-even nuclei around Z=120 and N=172, predicted to be spherical by the relativistic mean-field (RMF) model, are studied within a phenomenological collective approach. In the framework of the macroscopic model for giant resonances, we compute the transition densities of the isoscalar monopole, quadrupole, and octupole and isovector dipole modes for the superheavy nucleus ²⁹²120, whose ground-state density is determined from the RMF model. The results are also compared to those for²⁰⁸Pb.     

Scattering of <Emphasis Type="Italic">W</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> bosons at high-energy lepton colliders

We present a new study of quasi-elastic W and Z scattering processes in high-energy \(e^+e^-\) collisions, based on and extrapolating the low-energy effective theory which extends the standard model with a \(125\;\text {GeV}\) Higgs boson. We parameterize deviations in the low-energy range in terms of the dimension-eight operators that arise in the effective theory. Smoothly extending this to higher energy, we study a set of simplified models of new physics in W / Z scattering, (1) a structureless extrapolation of the effective theory, and (2) scalar and tensor resonance multiplets. The high-energy asymptotics of all models is regulated by a universal unitarization procedure. This enables us to provide benchmark scenarios which can be meaningfully evaluated off shell and in exclusive event samples, and to determine the sensitivity of an \(e^+e^-\) collider to the model parameters. We analyze the longitudinal vector-boson scattering modes, where we optimize the cuts for the fiducial cross section for different collider scenarios. Here, we choose energy stages of 1.0, 1.4 and 3 TeV, as motivated by the extendability of the ILC project and the staging scenario of the CLIC project.     

Single-particle properties of <Emphasis Type="Italic">N</Emphasis> = 12 to <Emphasis Type="Italic">N</Emphasis> = 20 silicon isotopes within the dispersive optical model

Experimental neutron and proton single-particle energies in N = 12 to N = 20 silicon isotopes and data on neutron and proton scattering by nuclei of the isotope ²⁸Si are analyzed on the basis of the dispersive optical model. Good agreement with available experimental data was attained. The occupation probabilities calculated for the single-particle states in question suggest a parallel-type filling of the 1d and 2s _1/2 neutron states in the isotopes ^{26,28,30,32,34}Si. The single-particle spectra being considered are indicative of the closure of the Z = 14 proton subshell in the isotopes ^30,32,34Si and the N = 20 neutron shell.     

Dynamics of the first-order magnetostructural transition in Gd<Subscript>5</Subscript>(Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>4</Subscript>

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian H in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M, (ii) atomic number Z, characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, . Since the thermodynamic quantities can be determined from H, we conclude that T _c , the superconducting transition temperature, when it is non-zero, may be formally expressed as T _c = . One piece of evidence in support is that, in an atomic number vs. atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) T _c is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C ₁₁, C ₁₂, and C ₄₄, the atomic weight and the atomic volume, and (b) T _c for five bcc transition metals is linear in the Cauchy deviation C ^* = (C ₁₂ - C ₄₄ )/(C ₁₂ + C ₄₄ ). Finally, via elastic constants, mass density and atomic volume, a correlation between C ^* and the Debye temperature is established for the five bcc transition elements.Received: 13 May 2004, Published online: 23 July 2004PACS: 74.62.-c Transition temperature variations - 74.70.Ad Metals; alloys and binary compounds     

<Emphasis Type="Italic">Z</Emphasis> lineshape versus fourth-generation masses

The dependence of the Z-resonance shape on the location of the threshold of the N\(\bar N\) production (N is the fourth-generation neutrino) is analyzed. The bounds on the existence of the fourth generation are derived from the comparison of the theoretical expression for the Z lineshape with the experimental data. The fourth generation is excluded at 95% C.L. for m _N <46.7±0.2 GeV.     

<Emphasis Type="Italic">Z</Emphasis><Superscript>0</Superscript>-boson decays in a strong electromagnetic field

The probability of Z ⁰-boson decay to a pair of charged fermions in a strong electromagnetic field, Z ⁰ → \(\bar f\) f, is calculated. On the basis of a method that employs exact solutions to relativistic wave equations for charged particles, an analytic expression for the partial decay width Γ(?) = Γ(Z ⁰ → \(\bar f\) f) is obtained at an arbitrary value of the parameter ? = \(eM_Z^{ - 3} \sqrt { - (F_{\mu \nu } q^\nu )^2 } \), which characterizes the external-field strength. The total Z ⁰-boson decay width in an intense electromagnetic field, Γ _Z (?), is calculated by summing these results over all known generations of charged leptons and quarks. It is found that, in the region of relatively weak fields (? < 0.06), the field-induced corrections to the standard Z ⁰-boson decay width in a vacuum do not exceed 2%. As ? increases, the total decay width Γ _Z (?) develops oscillations against the background of its gradual decrease to the absolute-minimum point. At ?_min = 0.445, the total Z ⁰-boson decay width reaches the minimum value of Γ _Z (?_min) = 2.164 GeV, which is smaller than the Z ⁰-boson decay width in a vacuum by more than 10%. In the region of superstrong fields (? > 1), Γ _Z (?) grows monotonically with increasing external-field strength. In the region ? > 5, the t-quark-production process Z ⁰ → \(\bar t\) t, which is forbidden in the absence of an external field, begins contributing significantly to the total decay width of the Z ⁰ boson.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Isospin mixing in the 4<Superscript> + </Superscript> doublet of <Superscript>54</Superscript><Emphasis Type="Italic">Co</Emphasis>

The T = 1 admixture into the T = 0 member of a recently discovered isospin-doublet in ⁵⁴Co is obtained from the measured electromagnetic E2/M1 multipole mixing ratio, of the transition. Combining these data with shell model calculations for strong isovector M1 and isoscalar E2 electromagnetic matrix elements one obtains a value for the T = 1 admixture into the T = 0, 4 ⁺ state of . The corresponding mixing matrix element in the 4 ⁺ doublet is keV.Received: 31 October 2002, Published online: 9 March 2004PACS: 21.10.Hw Spin, parity, and isobaric spin - 21.60.Cs Shell model - 23.20.Gq Multipole mixing ratios